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(Fine) Moduli (Spaces) For Linear Systems: What Are They And What Are They Good For

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  • Hazewinkel, M.

Abstract

This tutorial and . expository paper considers linear dynamical systems k = Fx + Gu, y = Hx, or, x(t+1) = Fx(t) + Gu(t), y(t) = Hx(t); more precisely it is really concerned with families of such, i.e., roughly speaking, with systems like the above where now the matrices F,G,H depend on some extra parameters a. After discussing some motivation for studying families (delay systems, systems over rings, n-d systems, perturbed systems, identification, parameter uncertainty) we discuss the classifying of families (fine moduli spaces). This is followed by two straightforward applications: realization with parameters and the nonexistence of global continuous canonical forms. More applications, especially to feedback will be discussed in Chris Byrnes' talks at this conference and similar problems as in these talks for networks will be discussed by Tyrone Duncan. The classifying fine moduli space cannot readily be extended and the concluding sections are devoted to this observation and a few more related results.

Suggested Citation

  • Hazewinkel, M., 1979. "(Fine) Moduli (Spaces) For Linear Systems: What Are They And What Are They Good For," Econometric Institute Archives 272181, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272181
    DOI: 10.22004/ag.econ.272181
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    Cited by:

    1. Hazewinkel, M., 1979. "A Partial Survey Of The Uses Of Algebraic Geometry In Systems And Control Theory," Econometric Institute Archives 272180, Erasmus University Rotterdam.

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